[GAP Forum] Minimal faithful permutation representation degree

[Hulpke,Alexander]

Dear Forum,

> 
> Let G be any finite group, let $\mu G$ be the minimal faithful permutation representation degree of G, all research papers  I got trying to investigate whether the inequality $\mu G\times \mu H \leq \mu G +\mu H$ is strict or equality, where H is any other group, I did the following and wish somebody explain;
> 
> 
> gap> a:=AlternatingGroup(5);:
> gap> IsPerfectGroup(a);
> true
> gap> s:=OneSmallGroup(46,IsSolvable,true);
> <pc group of size 46 with 2 generators>
> gap> D:=DirectProduct(s,a);
> <group of size 2760 with 4 generators>
> gap> mua:=MinimalFaithfulPermutationDegree(a);
> 5
> gap> mus:=MinimalFaithfulPermutationDegree(s);
> 23
> gap> muD:=MinimalFaithfulPermutationDegree(D);
> 33
> 

Thank you for reporting. This is a bug that will be corrected in a future release.

Regards,

  Alexander Hulpke